The unit of Newton's cooling constant is

Options

A. `(cal)/(sxx^(@)C)`
B. cal /s
C. `(cal)/(.^(@)C)`
D. `cal xxs xx^(@) C`

Answer

To determine the unit of Newton's cooling constant (k) in Newton's law of cooling, we can start by analyzing the equation given by Newton's law of cooling:

1. **Understanding the Equation**:
The equation is given as:
\[ \frac{dQ}{dt} = k (T - T_0) \]
where:
- \( \frac{dQ}{dt} \) is the rate of heat transfer (in calories per second),
- \( k \) is the Newton's cooling constant,
- \( T \) is the temperature of the object,
- \( T_0 \) is the ambient temperature.

2. **Identifying Units**:
- The unit of heat \( Q \) is in calories (Cal).
- The unit of time \( t \) is in seconds (s).
- The temperature difference \( (T - T_0) \) can be measured in degrees Celsius (°C) or Kelvin (K).

3. **Finding the Unit of \(\frac{dQ}{dt}\)**:
The unit of \( \frac{dQ}{dt} \) is:
\[ \text{Unit of } \frac{dQ}{dt} = \frac{\text{calories}}{\text{seconds}} = \text{Cal/s} \]

4. **Rearranging the Equation**:
To isolate \( k \), we can rearrange the equation:
\[ k = \frac{dQ/dt}{T - T_0} \]

5. **Substituting Units**:
Now, substituting the units into the equation:
\[ \text{Unit of } k = \frac{\text{Cal/s}}{\text{°C}} = \frac{\text{Cal}}{\text{s} \cdot \text{°C}} \]

6. **Conclusion**:
Therefore, the unit of Newton's cooling constant \( k \) is:
\[ \text{Cal/(s °C)} \]

### Summary of the Solution:
The unit of Newton's cooling constant is Cal/(s °C).